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@quinnj
Created Jul 7, 2020
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long double powers[] = {1.0e0L, 1.0e1L, 1.0e2L, 1.0e3L, 1.0e4L, 1.0e5L, 1.0e6L, 1.0e7L,
1.0e8L, 1.0e9L, 1.0e10L, 1.0e11L, 1.0e12L, 1.0e13L, 1.0e14L, 1.0e15L,
1.0e16L, 1.0e17L, 1.0e18L, 1.0e19L, 1.0e20L, 1.0e21L, 1.0e22L, 1.0e23L,
1.0e24L, 1.0e25L, 1.0e26L, 1.0e27L, 1.0e28L, 1.0e29L, 1.0e30L, 1.0e31L,
1.0e32L, 1.0e33L, 1.0e34L, 1.0e35L, 1.0e36L, 1.0e37L, 1.0e38L, 1.0e39L,
1.0e40L, 1.0e41L, 1.0e42L, 1.0e43L, 1.0e44L, 1.0e45L, 1.0e46L, 1.0e47L,
1.0e48L, 1.0e49L, 1.0e50L, 1.0e51L, 1.0e52L, 1.0e53L, 1.0e54L, 1.0e55L,
1.0e56L, 1.0e57L, 1.0e58L, 1.0e59L, 1.0e60L, 1.0e61L, 1.0e62L, 1.0e63L,
1.0e64L, 1.0e65L, 1.0e66L, 1.0e67L, 1.0e68L, 1.0e69L, 1.0e70L, 1.0e71L,
1.0e72L, 1.0e73L, 1.0e74L, 1.0e75L, 1.0e76L, 1.0e77L, 1.0e78L, 1.0e79L,
1.0e80L, 1.0e81L, 1.0e82L, 1.0e83L, 1.0e84L, 1.0e85L, 1.0e86L, 1.0e87L,
1.0e88L, 1.0e89L, 1.0e90L, 1.0e91L, 1.0e92L, 1.0e93L, 1.0e94L, 1.0e95L,
1.0e96L, 1.0e97L, 1.0e98L, 1.0e99L, 1.0e100L, 1.0e101L, 1.0e102L, 1.0e103L,
1.0e104L, 1.0e105L, 1.0e106L, 1.0e107L, 1.0e108L, 1.0e109L, 1.0e110L, 1.0e111L,
1.0e112L, 1.0e113L, 1.0e114L, 1.0e115L, 1.0e116L, 1.0e117L, 1.0e118L, 1.0e119L,
1.0e120L, 1.0e121L, 1.0e122L, 1.0e123L, 1.0e124L, 1.0e125L, 1.0e126L, 1.0e127L,
1.0e128L, 1.0e129L, 1.0e130L, 1.0e131L, 1.0e132L, 1.0e133L, 1.0e134L, 1.0e135L,
1.0e136L, 1.0e137L, 1.0e138L, 1.0e139L, 1.0e140L, 1.0e141L, 1.0e142L, 1.0e143L,
1.0e144L, 1.0e145L, 1.0e146L, 1.0e147L, 1.0e148L, 1.0e149L, 1.0e150L, 1.0e151L,
1.0e152L, 1.0e153L, 1.0e154L, 1.0e155L, 1.0e156L, 1.0e157L, 1.0e158L, 1.0e159L,
1.0e160L, 1.0e161L, 1.0e162L, 1.0e163L, 1.0e164L, 1.0e165L, 1.0e166L, 1.0e167L,
1.0e168L, 1.0e169L, 1.0e170L, 1.0e171L, 1.0e172L, 1.0e173L, 1.0e174L, 1.0e175L,
1.0e176L, 1.0e177L, 1.0e178L, 1.0e179L, 1.0e180L, 1.0e181L, 1.0e182L, 1.0e183L,
1.0e184L, 1.0e185L, 1.0e186L, 1.0e187L, 1.0e188L, 1.0e189L, 1.0e190L, 1.0e191L,
1.0e192L, 1.0e193L, 1.0e194L, 1.0e195L, 1.0e196L, 1.0e197L, 1.0e198L, 1.0e199L,
1.0e200L, 1.0e201L, 1.0e202L, 1.0e203L, 1.0e204L, 1.0e205L, 1.0e206L, 1.0e207L,
1.0e208L, 1.0e209L, 1.0e210L, 1.0e211L, 1.0e212L, 1.0e213L, 1.0e214L, 1.0e215L,
1.0e216L, 1.0e217L, 1.0e218L, 1.0e219L, 1.0e220L, 1.0e221L, 1.0e222L, 1.0e223L,
1.0e224L, 1.0e225L, 1.0e226L, 1.0e227L, 1.0e228L, 1.0e229L, 1.0e230L, 1.0e231L,
1.0e232L, 1.0e233L, 1.0e234L, 1.0e235L, 1.0e236L, 1.0e237L, 1.0e238L, 1.0e239L,
1.0e240L, 1.0e241L, 1.0e242L, 1.0e243L, 1.0e244L, 1.0e245L, 1.0e246L, 1.0e247L,
1.0e248L, 1.0e249L, 1.0e250L, 1.0e251L, 1.0e252L, 1.0e253L, 1.0e254L, 1.0e255L,
1.0e256L, 1.0e257L, 1.0e258L, 1.0e259L, 1.0e260L, 1.0e261L, 1.0e262L, 1.0e263L,
1.0e264L, 1.0e265L, 1.0e266L, 1.0e267L, 1.0e268L, 1.0e269L, 1.0e270L, 1.0e271L,
1.0e272L, 1.0e273L, 1.0e274L, 1.0e275L, 1.0e276L, 1.0e277L, 1.0e278L, 1.0e279L,
1.0e280L, 1.0e281L, 1.0e282L, 1.0e283L, 1.0e284L, 1.0e285L, 1.0e286L, 1.0e287L,
1.0e288L, 1.0e289L, 1.0e290L, 1.0e291L, 1.0e292L, 1.0e293L, 1.0e294L, 1.0e295L,
1.0e296L, 1.0e297L, 1.0e298L, 1.0e299L, 1.0e300L, 1.0e301L, 1.0e302L, 1.0e303L,
1.0e304L, 1.0e305L, 1.0e306L, 1.0e307L, 1.0e308L, INFINITY };
uint64_t pow5[] = {3362984268825341917L, 4203730336031677396L, 2627331460019798373L, 3284164325024747966L, 4105205406280934957L, 2565753378925584348L, 3207191723656980435L, 4008989654571225544L,
2505618534107015965L, 3132023167633769956L, 3915028959542212446L, 2446893099713882778L, 3058616374642353473L, 3823270468302941842L, 2389544042689338651L, 2986930053361673314L,
3733662566702091642L, 2333539104188807276L, 2916923880236009095L, 3646154850295011369L, 4557693562868764212L, 2848558476792977632L, 3560698095991222040L, 4450872619989027550L,
2781795387493142219L, 3477244234366427774L, 4346555292958034717L, 2716597058098771698L, 3395746322623464623L, 4244682903279330778L, 2652926814549581736L, 3316158518186977171L,
4145198147733721463L, 2590748842333575914L, 3238436052916969893L, 4048045066146212367L, 2530028166341382729L, 3162535207926728411L, 3953169009908410514L, 2470730631192756571L,
3088413288990945714L, 3860516611238682143L, 2412822882024176339L, 3016028602530220424L, 3770035753162775530L, 2356272345726734706L, 2945340432158418383L, 3681675540198022979L,
4602094425247528723L, 2876309015779705452L, 3595386269724631815L, 4494232837155789769L, 2808895523222368605L, 3511119404027960757L, 4388899255034950946L, 2743062034396844341L,
3428827542996055427L, 4286034428745069283L, 2678771517965668302L, 3348464397457085377L, 4185580496821356722L, 2615987810513347951L, 3269984763141684939L, 4087480953927106174L,
2554675596204441358L, 3193344495255551698L, 3991680619069439623L, 2494800386918399764L, 3118500483647999705L, 3898125604559999632L, 2436328502849999770L, 3045410628562499712L,
3806763285703124640L, 2379227053564452900L, 2974033816955566125L, 3717542271194457656L, 2323463919496536035L, 2904329899370670044L, 3630412374213337555L, 4538015467766671944L,
2836259667354169965L, 3545324584192712456L, 4431655730240890570L, 2769784831400556606L, 3462231039250695758L, 4327788799063369698L, 2704867999414606061L, 3381084999268257576L,
4226356249085321970L, 2641472655678326231L, 3301840819597907789L, 4127301024497384737L, 2579563140310865460L, 3224453925388581825L, 4030567406735727282L, 2519104629209829551L,
3148880786512286939L, 3936100983140358674L, 2460063114462724171L, 3075078893078405214L, 3843848616348006517L, 2402405385217504073L, 3003006731521880091L, 3753758414402350114L,
2346099009001468821L, 2932623761251836027L, 3665779701564795034L, 4582224626955993792L, 2863890391847496120L, 3579862989809370150L, 4474828737261712688L, 2796767960788570430L,
3495959950985713037L, 4369949938732141297L, 2731218711707588310L, 3414023389634485388L, 4267529237043106735L, 2667205773151941709L, 3334007216439927137L, 4167509020549908921L,
2604693137843693075L, 3255866422304616344L, 4069833027880770430L, 2543645642425481519L, 3179557053031851899L, 3974446316289814873L, 2484028947681134296L, 3105036184601417870L,
3881295230751772337L, 2425809519219857711L, 3032261899024822138L, 3790327373781027673L, 2368954608613142296L, 2961193260766427870L, 3701491575958034837L, 2313432234973771773L,
2891790293717214716L, 3614737867146518396L, 4518422333933147995L, 2824013958708217496L, 3530017448385271871L, 4412521810481589838L, 2757826131550993649L, 3447282664438742061L,
4309103330548427577L, 2693189581592767235L, 3366486976990959044L, 4208108721238698805L, 2630067950774186753L, 3287584938467733442L, 4109481173084666802L, 2568425733177916751L,
3210532166472395939L, 4013165208090494924L, 2508228255056559327L, 3135285318820699159L, 3919106648525873949L, 2449441655328671218L, 3061802069160839023L, 3827252586451048778L,
2392032866531905486L, 2990041083164881858L, 3737551353956102323L, 2335969596222563951L, 2919961995278204939L, 3649952494097756174L, 4562440617622195218L, 2851525386013872011L,
3564406732517340014L, 4455508415646675018L, 2784692759779171886L, 3480865949723964857L, 4351082437154956072L, 2719426523221847545L, 3399283154027309431L, 4249103942534136789L,
2655689964083835493L, 3319612455104794366L, 4149515568880992958L, 2593447230550620599L, 3241809038188275748L, 4052261297735344686L, 2532663311084590428L, 3165829138855738035L,
3957286423569672544L, 2473304014731045340L, 3091630018413806675L, 3864537523017258344L, 2415335951885786465L, 3019169939857233081L, 3773962424821541352L, 2358726515513463345L,
2948408144391829181L, 3685510180489786476L, 4606887725612233095L, 2879304828507645684L, 3599131035634557106L, 4498913794543196382L, 2811821121589497739L, 3514776401986872174L,
4393470502483590217L, 2745919064052243885L, 3432398830065304857L, 4290498537581631071L, 2681561585988519419L, 3351951982485649274L, 4189939978107061593L, 2618712486316913496L,
3273390607896141870L, 4091738259870177337L, 2557336412418860835L, 3196670515523576044L, 3995838144404470056L, 2497398840252793785L, 3121748550315992231L, 3902185687894990289L,
2438866054934368930L, 3048582568667961163L, 3810728210834951454L, 2381705131771844658L, 2977131414714805823L, 3721414268393507279L, 2325883917745942049L, 2907354897182427562L,
3634193621478034452L, 4542742026847543065L, 2839213766779714416L, 3549017208474643020L, 4436271510593303775L, 2772669694120814859L, 3465837117651018574L, 4332296397063773218L,
2707685248164858261L, 3384606560206072826L, 4230758200257591033L, 2644223875160994395L, 3305279843951242994L, 4131599804939053743L, 2582249878086908589L, 3227812347608635737L,
4034765434510794671L, 2521728396569246669L, 3152160495711558336L, 3940200619639447921L, 2462625387274654950L, 3078281734093318688L, 3847852167616648360L, 2404907604760405225L,
3006134505950506531L, 3757668132438133164L, 2348542582773833227L, 2935678228467291534L, 3669597785584114418L, 4586997231980143023L, 2866873269987589389L, 3583591587484486736L,
4479489484355608421L, 2799680927722255263L, 3499601159652819078L, 4374501449566023848L, 2734063405978764905L, 3417579257473456131L, 4271974071841820164L, 2669983794901137602L,
3337479743626422003L, 4171849679533027504L, 2607406049708142190L, 3259257562135177738L, 4074071952668972172L, 2546294970418107607L, 3182868713022634509L, 3978585891278293137L,
2486616182048933210L, 3108270227561166513L, 3885337784451458141L, 2428336115282161338L, 3035420144102701673L, 3794275180128377091L, 2371421987580235682L, 2964277484475294602L,
3705346855594118253L, 2315841784746323908L, 2894802230932904885L, 3618502788666131106L, 4523128485832663883L, 2826955303645414927L, 3533694129556768659L, 4417117661945960823L,
2760698538716225514L, 3450873173395281893L, 4313591466744102367L, 2695994666715063979L, 3369993333393829974L, 4212491666742287467L, 2632807291713929667L, 3291009114642412084L,
4113761393303015105L, 2571100870814384440L, 3213876088517980551L, 4017345110647475688L, 2510840694154672305L, 3138550867693340381L, 3923188584616675477L, 2451992865385422173L,
3064991081731777716L, 3831238852164722145L, 2394524282602951341L, 2993155353253689176L, 3741444191567111470L, 2338402619729444669L, 2923003274661805836L, 3653754093327257295L,
4567192616659071619L, 2854495385411919762L, 3568119231764899702L, 4460149039706124628L, 2787593149816327892L, 3484491437270409865L, 4355614296588012332L, 2722258935367507707L,
3402823669209384634L, 4253529586511730793L, 2658455991569831745L, 3323069989462289682L, 4153837486827862102L, 2596148429267413814L, 3245185536584267267L, 4056481920730334084L,
2535301200456458802L, 3169126500570573503L, 3961408125713216879L, 2475880078570760549L, 3094850098213450687L, 3868562622766813359L, 2417851639229258349L, 3022314549036572936L,
3777893186295716170L, 2361183241434822606L, 2951479051793528258L, 3689348814741910323L, 4611686018427387904L, 2882303761517117440L, 3602879701896396800L, 4503599627370496000L,
2814749767106560000L, 3518437208883200000L, 4398046511104000000L, 2748779069440000000L, 3435973836800000000L, 4294967296000000000L, 2684354560000000000L, 3355443200000000000L,
4194304000000000000L, 2621440000000000000L, 3276800000000000000L, 4096000000000000000L, 2560000000000000000L, 3200000000000000000L, 4000000000000000000L, 2500000000000000000L,
3125000000000000000L, 3906250000000000000L, 2441406250000000000L, 3051757812500000000L, 3814697265625000000L, 2384185791015625000L, 2980232238769531250L, 3725290298461914062L,
2328306436538696289L, 2910383045673370361L, 3637978807091712951L, 4547473508864641189L, 2842170943040400743L, 3552713678800500929L, 4440892098500626161L, 2775557561562891351L,
3469446951953614188L, 4336808689942017736L, 2710505431213761085L, 3388131789017201356L, 4235164736271501695L, 2646977960169688559L, 3308722450212110699L, 4135903062765138374L,
2584939414228211483L, 3231174267785264354L, 4038967834731580443L, 2524354896707237777L, 3155443620884047221L, 3944304526105059027L, 2465190328815661891L, 3081487911019577364L,
3851859888774471706L, 2407412430484044816L, 3009265538105056020L, 3761581922631320025L, 2350988701644575015L, 2938735877055718769L, 3673419846319648462L, 4591774807899560578L,
2869859254937225361L, 3587324068671531701L, 4484155085839414626L, 2802596928649634141L, 3503246160812042677L, 4379057701015053346L, 2736911063134408341L, 3421138828918010427L,
4276423536147513033L, 2672764710092195646L, 3340955887615244557L, 4176194859519055697L, 2610121787199409810L, 3262652233999262263L, 4078315292499077829L, 2548947057811923643L,
3186183822264904554L, 3982729777831130692L, 2489206111144456682L, 3111507638930570853L, 3889384548663213566L, 2430865342914508479L, 3038581678643135599L, 3798227098303919498L,
2373891936439949686L, 2967364920549937108L, 3709206150687421385L, 2318253844179638366L, 2897817305224547957L, 3622271631530684947L, 4527839539413356183L, 2829899712133347614L,
3537374640166684518L, 4421718300208355648L, 2763573937630222280L, 3454467422037777850L, 4318084277547222312L, 2698802673467013945L, 3373503341833767431L, 4216879177292209289L,
2635549485807630806L, 3294436857259538507L, 4118046071574423134L, 2573778794734014459L, 3217223493417518073L, 4021529366771897592L, 2513455854232435995L, 3141819817790544993L,
3927274772238181242L, 2454546732648863276L, 3068183415811079095L, 3835229269763848869L, 2397018293602405543L, 2996272867003006929L, 3745341083753758661L, 2340838177346099163L,
2926047721682623954L, 3657559652103279943L, 4571949565129099928L, 2857468478205687455L, 3571835597757109319L, 4464794497196386649L, 2790496560747741655L, 3488120700934677069L,
4360150876168346337L, 2725094297605216460L, 3406367872006520575L, 4257959840008150719L, 2661224900005094199L, 3326531125006367749L, 4158163906257959687L, 2598852441411224804L,
3248565551764031005L, 4060706939705038757L, 2537941837315649223L, 3172427296644561529L, 3965534120805701911L, 2478458825503563694L, 3098073531879454618L, 3872591914849318272L,
2420369946780823920L, 3025462433476029900L, 3781828041845037375L, 2363642526153148359L, 2954553157691435449L, 3693191447114294312L, 2308244654446433945L, 2885305818058042431L,
3606632272572553039L, 4508290340715691299L, 2817681462947307061L, 3522101828684133827L, 4402627285855167284L, 2751642053659479552L, 3439552567074349440L, 4299440708842936801L,
2687150443026835500L, 3358938053783544375L, 4198672567229430469L, 2624170354518394043L, 3280212943147992554L, 4100266178934990693L, 2562666361834369183L, 3203332952292961479L,
4004166190366201848L, 2502603868978876155L, 3128254836223595194L, 3910318545279493993L, 2443949090799683745L, 3054936363499604682L, 3818670454374505852L, 2386669033984066157L,
2983336292480082697L, 3729170365600103371L, 2330731478500064607L, 2913414348125080759L, 3641767935156350948L, 4552209918945438686L, 2845131199340899178L, 3556413999176123973L,
4445517498970154966L, 2778448436856346854L, 3473060546070433567L, 4341325682588041959L, 2713328551617526224L, 3391660689521907781L, 4239575861902384726L, 2649734913688990454L,
3312168642111238067L, 4140210802639047584L, 2587631751649404740L, 3234539689561755925L, 4043174611952194906L, 2526984132470121816L, 3158730165587652270L, 3948412706984565338L,
2467757941865353336L, 3084697427331691670L, 3855871784164614588L, 2409919865102884117L, 3012399831378605147L, 3765499789223256433L, 2353437368264535271L, 2941796710330669089L,
3677245887913336361L, 4596557359891670451L, 2872848349932294032L, 3591060437415367540L, 4488825546769209425L, 2805515966730755890L, 3506894958413444863L, 4383618698016806079L,
2739761686260503799L, 3424702107825629749L, 4280877634782037187L, 2675548521738773241L, 3344435652173466552L, 4180544565216833190L, 2612840353260520744L, 3266050441575650930L,
4082563051969563662L, 2551601907480977289L, 3189502384351221611L, 3986877980439027014L, 2491798737774391883L, 3114748422217989854L, 3893435527772487318L, 2433397204857804574L,
3041746506072255717L, 3802183132590319647L, 2376364457868949779L, 2970455572336187224L, 3713069465420234030L, 2320668415887646268L, 2900835519859557836L, 3626044399824447295L,
4532555499780559119L, 2832847187362849449L, 3541058984203561811L, 4426323730254452264L, 2766452331409032665L, 3458065414261290831L, 4322581767826613539L, 2701613604891633462L,
3377017006114541827L, 4221271257643177284L, 2638294536026985803L, 3297868170033732253L, 4122335212542165317L, 2576459507838853323L, 3220574384798566654L, 4025717980998208317L,
2516073738123880198L, 3145092172654850248L, 3931365215818562810L, 2457103259886601756L, 3071379074858252195L, 3839223843572815244L, 2399514902233009527L, 2999393627791261909L,
3749242034739077387L, 2343276271711923366L, 2929095339639904208L, 3661369174549880260L, 4576711468187350325L, 2860444667617093953L, 3575555834521367442L, 4469444793151709302L,
2793402995719818314L, 3491753744649772892L, 4364692180812216115L, 2727932613007635072L, 3409915766259543840L, 4262394707824429800L, 2663996692390268625L, 3329995865487835781L,
4162494831859794727L, 2601559269912371704L, 3251949087390464630L, 4064936359238080788L, 2540585224523800492L, 3175731530654750615L, 3969664413318438269L, 2481040258324023918L,
3101300322905029898L, 3876625403631287372L, 2422890877269554608L, 3028613596586943260L, 3785766995733679075L, 2366104372333549421L, 2957630465416936777L, 3697038081771170971L,
2310648801106981857L, 2888311001383727321L, 3610388751729659152L, 4512985939662073940L, 2820616212288796212L, 3525770265360995265L, 4407212831701244082L, 2754508019813277551L,
3443135024766596939L, 4303918780958246174L, 2689949238098903858L, 3362436547623629823L, 4203045684529537279L, 2626903552830960799L, 3283629441038700999L, 4104536801298376249L,
2565335500811485155L, 3206669376014356444L };
int shift5[] = {-1129, -1126, -1122, -1119, -1116, -1112, -1109, -1106,
-1102, -1099, -1096, -1092, -1089, -1086, -1082, -1079,
-1076, -1072, -1069, -1066, -1063, -1059, -1056, -1053,
-1049, -1046, -1043, -1039, -1036, -1033, -1029, -1026,
-1023, -1019, -1016, -1013, -1009, -1006, -1003, -999,
-996, -993, -989, -986, -983, -979, -976, -973,
-970, -966, -963, -960, -956, -953, -950, -946,
-943, -940, -936, -933, -930, -926, -923, -920,
-916, -913, -910, -906, -903, -900, -896, -893,
-890, -886, -883, -880, -876, -873, -870, -867,
-863, -860, -857, -853, -850, -847, -843, -840,
-837, -833, -830, -827, -823, -820, -817, -813,
-810, -807, -803, -800, -797, -793, -790, -787,
-783, -780, -777, -774, -770, -767, -764, -760,
-757, -754, -750, -747, -744, -740, -737, -734,
-730, -727, -724, -720, -717, -714, -710, -707,
-704, -700, -697, -694, -690, -687, -684, -680,
-677, -674, -671, -667, -664, -661, -657, -654,
-651, -647, -644, -641, -637, -634, -631, -627,
-624, -621, -617, -614, -611, -607, -604, -601,
-597, -594, -591, -587, -584, -581, -578, -574,
-571, -568, -564, -561, -558, -554, -551, -548,
-544, -541, -538, -534, -531, -528, -524, -521,
-518, -514, -511, -508, -504, -501, -498, -494,
-491, -488, -485, -481, -478, -475, -471, -468,
-465, -461, -458, -455, -451, -448, -445, -441,
-438, -435, -431, -428, -425, -421, -418, -415,
-411, -408, -405, -401, -398, -395, -391, -388,
-385, -382, -378, -375, -372, -368, -365, -362,
-358, -355, -352, -348, -345, -342, -338, -335,
-332, -328, -325, -322, -318, -315, -312, -308,
-305, -302, -298, -295, -292, -289, -285, -282,
-279, -275, -272, -269, -265, -262, -259, -255,
-252, -249, -245, -242, -239, -235, -232, -229,
-225, -222, -219, -215, -212, -209, -205, -202,
-199, -195, -192, -189, -186, -182, -179, -176,
-172, -169, -166, -162, -159, -156, -152, -149,
-146, -142, -139, -136, -132, -129, -126, -122,
-119, -116, -112, -109, -106, -102, -99, -96,
-93, -89, -86, -83, -79, -76, -73, -69,
-66, -63, -59, -56, -53, -49, -46, -43,
-39, -36, -33, -29, -26, -23, -19, -16,
-13, -9, -6, -3, 0, 4, 7, 10,
14, 17, 20, 24, 27, 30, 34, 37,
40, 44, 47, 50, 54, 57, 60, 64,
67, 70, 74, 77, 80, 84, 87, 90,
94, 97, 100, 103, 107, 110, 113, 117,
120, 123, 127, 130, 133, 137, 140, 143,
147, 150, 153, 157, 160, 163, 167, 170,
173, 177, 180, 183, 187, 190, 193, 196,
200, 203, 206, 210, 213, 216, 220, 223,
226, 230, 233, 236, 240, 243, 246, 250,
253, 256, 260, 263, 266, 270, 273, 276,
280, 283, 286, 290, 293, 296, 299, 303,
306, 309, 313, 316, 319, 323, 326, 329,
333, 336, 339, 343, 346, 349, 353, 356,
359, 363, 366, 369, 373, 376, 379, 383,
386, 389, 392, 396, 399, 402, 406, 409,
412, 416, 419, 422, 426, 429, 432, 436,
439, 442, 446, 449, 452, 456, 459, 462,
466, 469, 472, 476, 479, 482, 486, 489,
492, 495, 499, 502, 505, 509, 512, 515,
519, 522, 525, 529, 532, 535, 539, 542,
545, 549, 552, 555, 559, 562, 565, 569,
572, 575, 579, 582, 585, 588, 592, 595,
598, 602, 605, 608, 612, 615, 618, 622,
625, 628, 632, 635, 638, 642, 645, 648,
652, 655, 658, 662, 665, 668, 672, 675,
678, 681, 685, 688, 691, 695, 698, 701,
705, 708, 711, 715, 718, 721, 725, 728,
731, 735, 738, 741, 745, 748, 751, 755,
758, 761, 765, 768, 771, 775, 778, 781,
784, 788, 791, 794, 798, 801, 804, 808,
811, 814, 818, 821, 824, 828, 831, 834,
838, 841, 844, 848, 851, 854, 858, 861,
864, 868, 871, 874, 877, 881, 884, 887,
891, 894, 897, 901, 904, 907, 911, 914,
917, 921, 924, 927, 931, 934, 937, 941,
944, 947, 951, 954, 957, 961, 964, 967,
971, 974, 977, 980, 984, 987, 990, 994,
997, 1000, 1004, 1007, 1010, 1014, 1017, 1020,
1024, 1027 };
double pow2[] = {2.2250738585072014e-308, 4.4501477170144028e-308, 8.9002954340288055e-308, 1.7800590868057611e-307, 3.5601181736115222e-307, 7.1202363472230444e-307, 1.4240472694446089e-306, 2.8480945388892178e-306,
5.6961890777784355e-306, 1.1392378155556871e-305, 2.2784756311113742e-305, 4.5569512622227484e-305, 9.1139025244454969e-305, 1.8227805048890994e-304, 3.6455610097781987e-304, 7.2911220195563975e-304,
1.4582244039112795e-303, 2.916448807822559e-303, 5.832897615645118e-303, 1.1665795231290236e-302, 2.3331590462580472e-302, 4.6663180925160944e-302, 9.3326361850321888e-302, 1.8665272370064378e-301,
3.7330544740128755e-301, 7.466108948025751e-301, 1.4932217896051502e-300, 2.9864435792103004e-300, 5.9728871584206008e-300, 1.1945774316841202e-299, 2.3891548633682403e-299, 4.7783097267364807e-299,
9.5566194534729613e-299, 1.9113238906945923e-298, 3.8226477813891845e-298, 7.6452955627783691e-298, 1.5290591125556738e-297, 3.0581182251113476e-297, 6.1162364502226952e-297, 1.223247290044539e-296,
2.4464945800890781e-296, 4.8929891601781562e-296, 9.7859783203563124e-296, 1.9571956640712625e-295, 3.914391328142525e-295, 7.8287826562850499e-295, 1.56575653125701e-294, 3.13151306251402e-294,
6.2630261250280399e-294, 1.252605225005608e-293, 2.505210450011216e-293, 5.0104209000224319e-293, 1.0020841800044864e-292, 2.0041683600089728e-292, 4.0083367200179456e-292, 8.0166734400358911e-292,
1.6033346880071782e-291, 3.2066693760143564e-291, 6.4133387520287129e-291, 1.2826677504057426e-290, 2.5653355008114852e-290, 5.1306710016229703e-290, 1.0261342003245941e-289, 2.0522684006491881e-289,
4.1045368012983762e-289, 8.2090736025967525e-289, 1.6418147205193505e-288, 3.283629441038701e-288, 6.567258882077402e-288, 1.3134517764154804e-287, 2.6269035528309608e-287, 5.2538071056619216e-287,
1.0507614211323843e-286, 2.1015228422647686e-286, 4.2030456845295373e-286, 8.4060913690590746e-286, 1.6812182738118149e-285, 3.3624365476236298e-285, 6.7248730952472596e-285, 1.3449746190494519e-284,
2.6899492380989039e-284, 5.3798984761978077e-284, 1.0759796952395615e-283, 2.1519593904791231e-283, 4.3039187809582462e-283, 8.6078375619164923e-283, 1.7215675123832985e-282, 3.4431350247665969e-282,
6.8862700495331939e-282, 1.3772540099066388e-281, 2.7545080198132776e-281, 5.5090160396265551e-281, 1.101803207925311e-280, 2.203606415850622e-280, 4.4072128317012441e-280, 8.8144256634024882e-280,
1.7628851326804976e-279, 3.5257702653609953e-279, 7.0515405307219905e-279, 1.4103081061443981e-278, 2.8206162122887962e-278, 5.6412324245775924e-278, 1.1282464849155185e-277, 2.256492969831037e-277,
4.5129859396620739e-277, 9.0259718793241479e-277, 1.8051943758648296e-276, 3.6103887517296592e-276, 7.2207775034593183e-276, 1.4441555006918637e-275, 2.8883110013837273e-275, 5.7766220027674546e-275,
1.1553244005534909e-274, 2.3106488011069819e-274, 4.6212976022139637e-274, 9.2425952044279274e-274, 1.8485190408855855e-273, 3.697038081771171e-273, 7.3940761635423419e-273, 1.4788152327084684e-272,
2.9576304654169368e-272, 5.9152609308338736e-272, 1.1830521861667747e-271, 2.3661043723335494e-271, 4.7322087446670988e-271, 9.4644174893341977e-271, 1.8928834978668395e-270, 3.7857669957336791e-270,
7.5715339914673582e-270, 1.5143067982934716e-269, 3.0286135965869433e-269, 6.0572271931738865e-269, 1.2114454386347773e-268, 2.4228908772695546e-268, 4.8457817545391092e-268, 9.6915635090782184e-268,
1.9383127018156437e-267, 3.8766254036312874e-267, 7.7532508072625747e-267, 1.5506501614525149e-266, 3.1013003229050299e-266, 6.2026006458100598e-266, 1.240520129162012e-265, 2.4810402583240239e-265,
4.9620805166480478e-265, 9.9241610332960957e-265, 1.9848322066592191e-264, 3.9696644133184383e-264, 7.9393288266368765e-264, 1.5878657653273753e-263, 3.1757315306547506e-263, 6.3514630613095012e-263,
1.2702926122619002e-262, 2.5405852245238005e-262, 5.081170449047601e-262, 1.0162340898095202e-261, 2.0324681796190404e-261, 4.0649363592380808e-261, 8.1298727184761616e-261, 1.6259745436952323e-260,
3.2519490873904646e-260, 6.5038981747809293e-260, 1.3007796349561859e-259, 2.6015592699123717e-259, 5.2031185398247434e-259, 1.0406237079649487e-258, 2.0812474159298974e-258, 4.1624948318597947e-258,
8.3249896637195895e-258, 1.6649979327439179e-257, 3.3299958654878358e-257, 6.6599917309756716e-257, 1.3319983461951343e-256, 2.6639966923902686e-256, 5.3279933847805373e-256, 1.0655986769561075e-255,
2.1311973539122149e-255, 4.2623947078244298e-255, 8.5247894156488596e-255, 1.7049578831297719e-254, 3.4099157662595438e-254, 6.8198315325190877e-254, 1.3639663065038175e-253, 2.7279326130076351e-253,
5.4558652260152701e-253, 1.091173045203054e-252, 2.1823460904061081e-252, 4.3646921808122161e-252, 8.7293843616244322e-252, 1.7458768723248864e-251, 3.4917537446497729e-251, 6.9835074892995458e-251,
1.3967014978599092e-250, 2.7934029957198183e-250, 5.5868059914396366e-250, 1.1173611982879273e-249, 2.2347223965758547e-249, 4.4694447931517093e-249, 8.9388895863034186e-249, 1.7877779172606837e-248,
3.5755558345213674e-248, 7.1511116690427349e-248, 1.430222333808547e-247, 2.860444667617094e-247, 5.7208893352341879e-247, 1.1441778670468376e-246, 2.2883557340936752e-246, 4.5767114681873503e-246,
9.1534229363747007e-246, 1.8306845872749401e-245, 3.6613691745498803e-245, 7.3227383490997605e-245, 1.4645476698199521e-244, 2.9290953396399042e-244, 5.8581906792798084e-244, 1.1716381358559617e-243,
2.3432762717119234e-243, 4.6865525434238467e-243, 9.3731050868476935e-243, 1.8746210173695387e-242, 3.7492420347390774e-242, 7.4984840694781548e-242, 1.499696813895631e-241, 2.9993936277912619e-241,
5.9987872555825238e-241, 1.1997574511165048e-240, 2.3995149022330095e-240, 4.7990298044660191e-240, 9.5980596089320381e-240, 1.9196119217864076e-239, 3.8392238435728152e-239, 7.6784476871456305e-239,
1.5356895374291261e-238, 3.0713790748582522e-238, 6.1427581497165044e-238, 1.2285516299433009e-237, 2.4571032598866018e-237, 4.9142065197732035e-237, 9.828413039546407e-237, 1.9656826079092814e-236,
3.9313652158185628e-236, 7.8627304316371256e-236, 1.5725460863274251e-235, 3.1450921726548502e-235, 6.2901843453097005e-235, 1.2580368690619401e-234, 2.5160737381238802e-234, 5.0321474762477604e-234,
1.0064294952495521e-233, 2.0128589904991042e-233, 4.0257179809982083e-233, 8.0514359619964166e-233, 1.6102871923992833e-232, 3.2205743847985667e-232, 6.4411487695971333e-232, 1.2882297539194267e-231,
2.5764595078388533e-231, 5.1529190156777066e-231, 1.0305838031355413e-230, 2.0611676062710827e-230, 4.1223352125421653e-230, 8.2446704250843306e-230, 1.6489340850168661e-229, 3.2978681700337323e-229,
6.5957363400674645e-229, 1.3191472680134929e-228, 2.6382945360269858e-228, 5.2765890720539716e-228, 1.0553178144107943e-227, 2.1106356288215886e-227, 4.2212712576431773e-227, 8.4425425152863546e-227,
1.6885085030572709e-226, 3.3770170061145418e-226, 6.7540340122290837e-226, 1.3508068024458167e-225, 2.7016136048916335e-225, 5.4032272097832669e-225, 1.0806454419566534e-224, 2.1612908839133068e-224,
4.3225817678266135e-224, 8.6451635356532271e-224, 1.7290327071306454e-223, 3.4580654142612908e-223, 6.9161308285225817e-223, 1.3832261657045163e-222, 2.7664523314090327e-222, 5.5329046628180653e-222,
1.1065809325636131e-221, 2.2131618651272261e-221, 4.4263237302544523e-221, 8.8526474605089045e-221, 1.7705294921017809e-220, 3.5410589842035618e-220, 7.0821179684071236e-220, 1.4164235936814247e-219,
2.8328471873628494e-219, 5.6656943747256989e-219, 1.1331388749451398e-218, 2.2662777498902796e-218, 4.5325554997805591e-218, 9.0651109995611182e-218, 1.8130221999122236e-217, 3.6260443998244473e-217,
7.2520887996488946e-217, 1.4504177599297789e-216, 2.9008355198595578e-216, 5.8016710397191157e-216, 1.1603342079438231e-215, 2.3206684158876463e-215, 4.6413368317752925e-215, 9.2826736635505851e-215,
1.856534732710117e-214, 3.713069465420234e-214, 7.4261389308404681e-214, 1.4852277861680936e-213, 2.9704555723361872e-213, 5.9409111446723744e-213, 1.1881822289344749e-212, 2.3763644578689498e-212,
4.7527289157378996e-212, 9.5054578314757991e-212, 1.9010915662951598e-211, 3.8021831325903196e-211, 7.6043662651806393e-211, 1.5208732530361279e-210, 3.0417465060722557e-210, 6.0834930121445114e-210,
1.2166986024289023e-209, 2.4333972048578046e-209, 4.8667944097156091e-209, 9.7335888194312183e-209, 1.9467177638862437e-208, 3.8934355277724873e-208, 7.7868710555449746e-208, 1.5573742111089949e-207,
3.1147484222179899e-207, 6.2294968444359797e-207, 1.2458993688871959e-206, 2.4917987377743919e-206, 4.9835974755487838e-206, 9.9671949510975675e-206, 1.9934389902195135e-205, 3.986877980439027e-205,
7.973755960878054e-205, 1.5947511921756108e-204, 3.1895023843512216e-204, 6.3790047687024432e-204, 1.2758009537404886e-203, 2.5516019074809773e-203, 5.1032038149619546e-203, 1.0206407629923909e-202,
2.0412815259847818e-202, 4.0825630519695637e-202, 8.1651261039391273e-202, 1.6330252207878255e-201, 3.2660504415756509e-201, 6.5321008831513019e-201, 1.3064201766302604e-200, 2.6128403532605207e-200,
5.2256807065210415e-200, 1.0451361413042083e-199, 2.0902722826084166e-199, 4.1805445652168332e-199, 8.3610891304336664e-199, 1.6722178260867333e-198, 3.3444356521734666e-198, 6.6888713043469331e-198,
1.3377742608693866e-197, 2.6755485217387732e-197, 5.3510970434775465e-197, 1.0702194086955093e-196, 2.1404388173910186e-196, 4.2808776347820372e-196, 8.5617552695640744e-196, 1.7123510539128149e-195,
3.4247021078256297e-195, 6.8494042156512595e-195, 1.3698808431302519e-194, 2.7397616862605038e-194, 5.4795233725210076e-194, 1.0959046745042015e-193, 2.191809349008403e-193, 4.3836186980168061e-193,
8.7672373960336122e-193, 1.7534474792067224e-192, 3.5068949584134449e-192, 7.0137899168268897e-192, 1.4027579833653779e-191, 2.8055159667307559e-191, 5.6110319334615118e-191, 1.1222063866923024e-190,
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0.015625, 0.03125, 0.0625, 0.125, 0.25, 0.5, 1, 2,
4, 8, 16, 32, 64, 128, 256, 512,
1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072,
262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432,
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